Question: Solve for $x$ and $y$ using elimination. ${6x+4y = 84}$ ${2x+3y = 38}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${6x+4y = 84}$ $-6x-9y = -114$ Add the top and bottom equations together. $-5y = -30$ $\dfrac{-5y}{{-5}} = \dfrac{-30}{{-5}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {6x+4y = 84}\thinspace$ to find $x$ ${6x + 4}{(6)}{= 84}$ $6x+24 = 84$ $6x+24{-24} = 84{-24}$ $6x = 60$ $\dfrac{6x}{{6}} = \dfrac{60}{{6}}$ ${x = 10}$ You can also plug ${y = 6}$ into $\thinspace {2x+3y = 38}\thinspace$ and get the same answer for $x$ : ${2x + 3}{(6)}{= 38}$ ${x = 10}$